Four particles each of mass $m$ are placed at the vertices of a square of side $l$. What is the grav

Question

Four particles each of mass $m$ are placed at the vertices of a square of side $l$. What is the gravitational potential at the centre of the square?

Professor PC Thomas Classes · Answer

The distance from the centre to each vertex is $r = \frac{l}{\sqrt{2}}$. The total potential at the centre is the sum of potentials due to the 4 masses: $V = 4 	imes (-\frac{Gm}{r}) = -4\frac{Gm}{l/\sqrt{2}} = -4\sqrt{2}\frac{Gm}{l}$.